Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26021879 | C2 | semidirect |
| 3. #26021873 | C2 | semidirect |
| 4. #26018331 | C2 | semidirect |
| 5. C89×#3407 | C2 | semidirect |
| 54. C2×C16×C89 | D4 | semidirect |
| 143. #3407 | D89 | semidirect |
| 148. C89 | #12988 | semidirect |
| 192. C2×C16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028968 | 2 |
| #26021879 | 2 |
| #26021873 | 2 |
| #26018331 | 2 |
| C89×#3407 | 2 |
| #12988 | 89 |